In the final verses of Psalm 26, David contrasts himself with 'sinners' and speaks of his own 'integrity' (as in earlier verses where he says: "I have walked in my integrity" and "I wash my hands in innocence").

9Do not sweep my soul away with sinners,
nor my life with bloodthirsty men,10in whose hands are evil devices,
and whose right hands are full of bribes.11But as for me, I shall walk in my integrity;redeem me, and be gracious to me.12My foot stands on level ground;
in the great assembly I will bless the LORD. Psalm 26:9-12 ESV

In my understanding of grace and sin, if David is not a 'sinner' then he has no need of grace - but David is clearly not using those words in quite the same way.

So how should we understand the words 'gracious' (and 'redeem'), and 'sinner' in this context?

1 Answer
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"Grace", "redemption" and "sin" are different on the OT, and are used without a framework of theological doctrine. Indeed, there isn't much doctrine or systematic theology at all in the OT. That type of thinking came later.

Grace here is "chen", a word meaning good favor, the believer's version of "good luck". see for example the priestly blessing. We all want and need this, without connection to anything we have done. See Exodus 11:3 for and example of the word used in a human context. Also Exodus 33:12.

"Redemption" here is simple earthly redemption in the sense of Exodus 13:13 - an item, animal of person earmarked of sacrifice is allowed to live another day - keep me free of accidents, sickness and other misfortunes.

The sinners here are people who are not righteous, they have no conscience or they are not responsible, see Psalms 1:1. The writer does not consider himself to be one of them, quite the opposite, even though he does acknowledge his own transgressions.

"Integrity" here is the translation for "tam" or "tmimute", meaning without ulterior motive or without pretension, innocence. (It can also mean "pure", and is used to describe and animal without blemish fit for sacrifice.) Same word used for Noah in Gen 5:9, Jacob in Gen 25:27. Not really clear to me how your translator got to "integrity" in this context. "tmime darech" is the usual expression for integrity, see Proverbs 11:20.

This psalm gives a strong impression of very earthy, sincere reverence and supplication, refreshingly bereft of theology or doctrine.